The keyword is "Asynchronous".
It simply means, you can send data to, and retrieve data from, a server in the background. While waiting for response of the server, user can still use the web page as usual without a complete page refresh or interruption.
Despite the technology was first created by Microsoft for its Outlook Web Access (basically a web mail version of Microsoft Exchange), but Google was the company that surpised the world of Ajax techniques in Google Suggest, Google Maps and Gmail.
Despite the name, the use of XML is not neccessary required, ironically, JSON is a more favorable variant.